RICARDIAN RENTS, ENVIRONMENTAL POLICY
AND THE ‘DOUBLE-DIVIDEND’ HYPOTHESIS
Antonio M. Bento
School of Public Policy and National Center for Smart Growth
University of Maryland, College Park, MD 20742, USA
abento1@umd.edu
Mark Jacobsen
Department of Economics
Stanford University, Stanford, CA 94305-6072, USA
mrj@stanford.edu
_____________________________________________________________________
Abstract
Recent studies on the so-called double dividend hypothesis find that environmental tax swaps
exacerbate the costs of the tax system and therefore do not produce a double dividend. We extend
these models by incorporating a fixed-factor in the production of the polluting good and,
therefore, allowing Ricardian rents to be generated in the economy. In this setting, an
environmental tax reform with revenues used to cut pre-existing labor taxes can produce a double
dividend. Moreover, the overall costs of environmental tax swaps are negative up to 11 percent of
emissions reductions, suggesting the potential for a strong double dividend and confirming that
environmental taxes should be part of the optimal tax system.
_____________________________________________________________________
JEL Classification: D62, H21, H23
Key Words: Ricardian Rents, Environmental Taxation, Double-Dividend Hypothesis
2
1. Introduction
A growing number of analytical and numerical studies have cast doubt on the
validity of the double dividend hypothesis that is the claim that environmental taxes
could simultaneously improve environmental quality and increase the efficiency of the
tax system (e.g. Bovenberg and deMooij [1], Parry [8], Bovenberg and Goulder [2],
Goulder et. al. [6]).1 Two welfare effects underlie these results. First, by driving up the
price of (polluting) goods relative to leisure, environmental policies tend to compound
the factor-market distortions created by pre-existing labor taxes, thereby producing a
negative welfare impact termed the tax-interaction effect. Second, environmental taxes
whose revenues are recycled through cuts in marginal tax rates reduce the distortions
caused by the pre-existing taxes, which contributes to a positive welfare impact. Because
this revenue-recycling effect is not strong enough to compensate for the tax-interaction
effect, environmental tax swaps typically exacerbate rather than decrease the gross
efficiency costs of the tax system. As a consequence, there is no double dividend from an
environmental tax reform. A related point is that the second best environmental tax
should typically be set below the (first best) Pigouvian tax.2
These models typically assume that the production of all goods exhibits constant
returns to scale, with labor being in most cases the unique input in production.3 However,
certain types of environmental taxes are imposed on goods whose production is intensive
1
For an excellent survey of the double dividend literature, see Bovenberg and Goulder [3].
Parry and Bento [10], Parry and Bento [11], Williams [14] and Williams [15] examine special cases under
which the double dividend may occur.
3
An exception is the study by Bovenberg and Goulder [2]. In this study the authors consider several
intermediate inputs including fossil fuels, but don’t model the effects of Ricardian rents explicitly.
2
3
in exhaustible resources, with owners of these factors earning rents. In this case, unless
rents are fully exhausted, the tax system is not optimal to begin with, even from a nonenvironmental perspective.4
This naturally raises the question of whether the presence of fixed factors in
production and the potential existence of untaxable Ricardian rents makes it possible for
a double dividend to occur. This paper extends previous literature by asking the following
two questions: First, what are the implications of fixed factors in production of dirty
goods for the magnitude and sign of the first and second dividends? By first dividend we
mean the welfare gain from improving environmental quality; by second dividend we
mean the reduction in the costs of the tax system, when environmental tax revenues are
recycled to reduce the rate of a pre-existing labor tax. Second, in the presence of fixed
factors in the production of dirty goods, how does the second best optimal environmental
tax compare to the Pigouvian (first-best) tax? To answer these questions, we model a
static economy where households allocate their time between leisure and labor supply.
Labor, along with an exhaustible natural resource (i.e. coal), is used to produce a dirty
good.5 Our work is closely related to and complements recent studies by Perrori and
Whaley [12] and Williams [13]. Perrori and Whaley [12] investigate the significance of
rents for both the welfare costs and the optimal design of commodity taxes. Williams [13]
examines the costs of trade policies in a two sector model with sector-specific factors.
4
It is well established in the public finance literature that, in the presence of fixed factors in production, a
uniform commodity tax (or equivalently a labor tax) is not optimal. By not taxing more heavily the good
whose production has a fixed factor, a uniform commodity tax system fails to fully capture the rents from
this factor of production.
5
Coal is just used as an example of an exhaustible natural resource used in the production of a dirty good.
Other examples include resources like metals and cement. Further, there are likely additional costs
associated with rents including rents accruing to quasi-fixed capital investments, such as depreciated coal
generating facilities.
4
We find that a revenue-neutral shift towards an environmental tax produces a
double dividend. However, and interestingly, we find that there is a substantial tradeoff
between the magnitude of the first and the second dividend. In particular, in the presence
of a fixed factor in the production of the dirty good an environmental tax is not fully
passed to the final price of the dirty good, and hence we find that fixed factors in
production can substantially compromise the magnitude of the first dividend. However,
and to the extent that the environmental tax is not fully passed to the final price of the
polluting good, we also find that the tax interaction effect is not as strong as predicted by
previous literature. In our benchmark simulations, ignoring any environmental benefits,
the net impact of an environmental tax swap is to reduce the economic costs of the tax
system for pollution reductions up to at least 50%. In other words the general equilibrium
gross costs of the policy are less than the partial equilibrium costs, and by a substantial
amount. Indeed the overall costs of pollution reduction are negative for taxes that reduce
pollution by 11 percent, suggesting that even if there is uncertainty about the benefits
from the environmental policy, the environmental tax should be part of the tax system. A
related point is that, in contrast to typical results from earlier studies, we find the optimal
environmental tax may easily exceed the Pigouvian tax.
We also explore the implications of fixed factors and Ricardian rents for the costs
of other policy instruments. We find that the costs of non-auctioned pollution emissions
permits relative to emissions taxes can be significantly greater. This is due to the larger
effect from using revenues from environmental policies to reduce labor taxes in the
presence of fixed factors in the production of polluting goods.
5
The rest of the paper is organized as follows. Section 2 introduces the analytical
model and decomposes the general equilibrium welfare effects of an environmental tax
into its different components. Section 3 describes the simulation model and section 4
presents the simulation results. Section 5 offers conclusions.
2. The analytical model
A. Model Assumptions
We develop a static model in which a representative household enjoys utility from
a polluting good ( X ) , a non-polluting consumption good (Y ) and non-market time or
_
leisure. Leisure is equal to the household time endowment ( L) less labor supply (L) .
Emissions (E ) from producing X cause environmental damages in the form of reduced
consumer utility. The household utility function is given by:
_
U = u ( X , Y , L L) ( E )
(2.1)
u (.) is utility from non-environmental goods and is quasi-concave. (.) is disutility from
waste emissions and is weakly convex. In our model, we have abstracted from abatement
technologies, and therefore treat emissions as proportional to X .
The separability
restriction in (2.1) implies that the demands for X , Y and labor supply do not vary with
changes in E .
X and Y are produced by competitive firms. Labor is the only input in production
of Y . We assume the marginal product of labor is constant in this industry, and normalize
output to imply a marginal product (and wage rate) of unity. This normalization implies
that the unit cost of producing Y is unity.
6
Y = Y ( LY )
(2.2)
In contrast, two inputs are used in the production of X , labor and a fixed factor (Z ) :
X = X ( LX , Z )
(2.3)
where LX denotes the amount of labor used in the production of X . X exhibits
decreasing returns to scale with respect to LX . As a consequence, positive Ricardian rents
are earned by the owners of the fixed factor (Z ) . In the absence of an environmental
policy, rents are given by:
I = p X X vL
(2.4)
where p X and v denote producer price of good X and gross wage respectively.
The government levies a proportional tax of t L on labor earnings, regulates
emissions with an environmental tax (t E ) , and provides a fixed lump-sum transfer G to
households. We assume that the government budget balances; any revenue consequences
of environmental policies are offset by adjusting t L . We also assume that all rents
(I ) generated from the production of X are earned by the representative consumer. For
expositional reasons, in the analytical model we have abstracted from the possibility that
government can tax rents directly. We relax this assumption in the numerical model. The
household budget constraint is:
p X X + Y = (v t L ) L + I + G
(2.5)
where p X is the demand price of X . Households choose X , Y and L to maximize utility
(2.2) subject to the budget constraint (2.5), taking environmental damages as given. From
the resulting first-order conditions and (2.5) we obtain the uncompensated demand and
labor supply functions:
7
X ( p X , t L , I ) ; Y ( p X , t L , I ) ; L( p X , t L , I )
(2.6)
Substituting these equations into (2.2) gives the indirect utility function:
V = v( pX ,w,I) (E)
(2.7)
where w denotes the net wage rate.
With this framework we can now analyze the efficiency effects of a revenueneutral environmental tax reform.
B. The Welfare Effects of an Environmental Tax Reform
Consider a revenue-neutral tax of t E imposed on X , with revenues from this tax
employed to finance cuts in the distortionary tax, t L . The government holds the level of
G fixed and solves the budget constraint by adjusting t L :
tE E + tL L = G
(2.8)
The welfare effect of an incremental increase in the environmental tax with
revenues used to reduce the labor tax can be expressed as:6
1 dV ' dp X dX dI
dL
+
= + tL
dt E dt E dt E dt E
dt E
R
WP
where
(2.9)
WL
W
'
is the marginal external cost of pollution. The first term on the right-hand side
of equation (2.9), denoted by W P , comprises the Pigouvian welfare effect of this policy.
This is the efficiency gain associated with household’s responding to the higher price of
X induced by the emissions tax by substituting away from X to other goods and leisure.
6
We have arrived at (2.9) by totally differentiating the indirect utility function in (2.7) and the government
budget constraint in (2.8), while making use of Roy’s identity. A detailed derivation is available from the
authors upon request.
8
This effect equals the reduction in consumption of X multiplied by the wedge between
the marginal external cost and the increase in the price of the polluting good (due to the
marginal increase in the environmental tax), net of the primary economic costs of the
policy.7 W R is the rent effect. It represents a loss in real income to the household due to a
reduction in the Ricardian rents. This effect occurs because part of the burden of the
environmental tax falls on the fixed factor in the production of X . Finally, the term
W L represents the impact of a marginal increase in the environmental tax in the labor
market. This effect is given by the change in labor supply multiplied by the tax wedge
between the gross and net wage created by the pre-existing labor tax. There is a welfare
gain (or loss) in the labor market if the general equilibrium impact of the policy is to
increase (or decrease) labor supply. By differentiating (2.5) when G is constant, we can
further decompose this effect into the following three components:
L dp X L dt L L dI
dL
=
+
+
dt E p X dt E t L dt E I dt E
dW TI
dW RR
(2.10)
dW Rent
The term labeled dW TI represents the efficiency loss from the tax interaction
effect. The environmental tax increases the price of X , implying an increase in the cost of
consumption and thus a reduction in real wage. The term labeled dW RR is the efficiency
gain from the (marginal) revenue-recycling effect. It represents the efficiency gain
associated with using the revenues from the environmental tax to finance cuts in
distortionary taxes. Finally, the term labeled dW Re nt denotes the welfare effect from using
7
We define primary economic costs of the policy as the marginal costs in a first-best case when we set preexisting taxes and the level of the fixed factor to zero
9
the environmental tax as a ‘surrogate’ tax on Ricardian rents. Effectively, it is the case
that the environmental tax produces a tax shift away from labor towards fixed factors in
the production of polluting goods. To the extent that a marginal increase in the
environmental tax reduces rents, and in turn overall household income, households
increase labor supply at the margin. This effect produces an additional welfare gain in the
labor market that weakens the tax interaction effect and goes in the same direction of the
revenue-recycling effect. Note that even if the reduction of rents has no effect on labor
supply, the revenue recycling and rent effects (dWRR in equation 2.10 and WR in 2.09,
respectively) will still be present and continue to drive our main result.8 All three of the
effects act in the same direction, increasing the optimal tax above the Pigouvian level.
C. Relation to Previous Literature
In many previous studies (e.g. Bovenberg and deMooij [1], Parry [8], Goulder et.
al. [6] and Williams [14]) all goods are (ultimately) produced by labor, and therefore
these models do not account for the possibility that certain polluting goods use fixed
factors in their production generating Ricardian rents in the economy. The general
equilibrium welfare effects of a revenue neutral environmental tax in this context consist
of the Pigouvian welfare effect, the tax interaction effect, and the revenue-recycling
effect. These studies typically find that the tax-interaction effect dominates the revenuerecycling effect, and therefore the net impact of the environmental tax swap is to reduce
labor supply and increase the costs of pre-existing taxes. Not surprisingly, these studies
8
This might be the case in certain heterogeneous agent models, for example, where the agents earning the
rents are fully insulated from the labor market.
10
cast doubt on the “double dividend hypothesis”, that is the claim that an environmental
tax could both improve the environment and reduce the costs of the tax system.
The key insight from introducing sector-specific factors in the classical model of
environmental tax reform is that, as a consequence, the environmental tax will not be
fully passed to households in the form of higher consumer demand prices (as in the
previous models). Indeed, it is the case that, in the presence of fixed factors in
production:
dp X
<1
dt E
(2.11)
This suggests that the burden of the environmental tax is divided into two
channels in the economy: Part of the environmental tax will be translated into higher
prices of the polluting good, and second, part of the environmental tax will fall on the
fixed factor extracting some of its rents.9 This simple insight sheds light on several
important points central to the double-dividend debate.
First, let us consider the implications of our model to the first dividend and the
primary economic costs of the policy. We remind the reader that the “first dividend” is
the claim that a marginal increase in the environmental tax will improve environmental
quality. Before we proceed with this discussion, we also note that, perhaps surprisingly,
previous literature focused exclusively on the direction and magnitude of the second
dividend and took the first dividend for granted.10 In fact, because the environmental tax
would be fully passed to households in the form of higher polluting good prices, the first
9
Since the good is produced competitively, the burden of the tax will fall on the factors of production. The
portion of the tax falling on the scarce resource will be realized in the form of reduced Ricardian rents and
depends on the share of resource use and elasticity of substitution.
10
An exception is Koskela et al. [7]. In their model, firms choose clean and dirty factors of production, and
there is unemployment.
11
dividend would simply be the reduction in consumption of the polluting good multiplied
by the wedge between the marginal external cost of pollution and the environmental tax,
net of the primary cost of the policy. In contrast, our model suggests (see equations (2.8)
and (2.10)) that the magnitude of the first dividend can be substantially compromised in
the presence of fixed factors. This is because the increase in the price of the polluting
good is not given by the full amount of the tax and, as a consequence, for the same
marginal increase in the environmental tax, the total reduction in the consumption of the
polluting good is smaller in our model compared to previous models in the literature.
A second implication of our model is that the primary economic costs of the
policy will be higher than previously recognized in the literature. Again, this is because in
order to achieve the same level of emissions reductions, the level of the environmental
tax will need to be higher in our model, since part of the environmental tax falls on the
fixed factor. A related implication is that the environmental tax (at a given level) is a less
effective pollution reducing instrument, which should also be taken into consideration
when choosing amongst different policy instruments.
Next, let us consider the implications of our model to the second dividend and the
design of the optimal tax system. We remind the reader that by second dividend we mean
an overall reduction of the costs of the tax system when the revenues from the
environmental tax are used to cut pre-existing distortionary input taxes. Equations (2.8)
and (2.10) suggest that previous studies may have overestimated the magnitude of the tax
interaction effect. Again, to the extent that the environmental tax will not be fully passed
to households in the form of higher consumption prices, the reduction in real wage will
not be as drastic as previously suggested. Second, by shifting taxes away from labor into
12
the fixed factor and therefore reducing real income (through reductions in Ricardian
rents), environmental tax reforms may even create an incentive to increase labor supply at
the margin, which may have been overlooked in previous literature. This later effect will
certainly weaken the tax interaction effect and makes it more likely that the second
dividend be positive. We also note that, to the extent that part of the environmental tax is
effectively taxing Ricardian rents, the environmental tax should be part of the optimal tax
system, even from a non-environmental perspective. Therefore there are prospects for a
double dividend.
We conclude this section by noting that, in a sense, there is an interesting conflict
between the first and second dividend. Equations (2.8) and (2.10) above suggest that the
first dividend is maximized in the absence of fixed factors while, in contrast, the second
dividend would be maximized in the presence of fixed factors. In other words, from the
perspective of reducing pollution, it is desirable that the environmental tax raises the
price of the polluting good by its total amount. In contrast, if the goal is to reduce the
costs of the tax system, it is desirable that the environmental tax falls as much as possible
on the fixed factor, since this would get us closer to the optimal tax rule.
d. Optimal Environmental Tax
In the context of the double-dividend debate, a controversial issue that has
received substantial attention in the literature is the relation between the optimal second
best environmental tax and the traditional (first best) Pigouvian tax. Because previous
literature typically cast doubt on the existence of a double dividend, the resulting optimal
13
second best environmental tax lies below the Pigouvian tax. In this section, we reexamine this issue in the context of our model.
To obtain the optimal environmental tax, we set equation (2.10) equal to zero and
solve for
dp X
. The optimal environmental tax t E* is the tax that raises the price of the
dt E
polluting good by:
dL
dI
dp X '
dt E
dt E
= tL
dX
dX
dt E
dt E
dt E
(2.12)
First, note that in the absence of pre-existing labor taxes and Ricardian rents from
fixed factors in the production of the polluting good, the optimal environmental tax
should be set solely based on Pigouvian considerations. From a first best (Pigouvian)
perspective, the tax should be set equal to the dollar amount of the marginal external
costs of pollution.
As discussed above, it is not possible to sign the term
dL
, that is, the general
dt E
equilibrium impact of the environmental tax on the labor market. If it is the case that
labor supply increases in response to the environmental tax then the second term in
equation (2.12) suggests an increase in the environmental tax above and beyond its
Pigouvian level. Finally, the third term in equation (2.12) is unambiguously positive,
suggesting that the presence of fixed factors in polluting industries call for higher
environmental taxes, since the environmental tax is, in this case, effectively serving as a
‘surrogate’ to a Ricardian rent tax. This last term suggests that, from an optimal tax rule
perspective, the environmental tax should be part of the tax system.
14
We conclude this section by noting that it is not possible to say a priori whether
the optimal environmental tax should lie below or above the (first-best) Pigouvian tax. It
is certainly the case, however, that the optimal second best environmental tax should be
greater than recognized in the literature, reflecting the contribution of the third term in
equation (2.12) to the optimal level of the tax.
3. Simulation Model
In this section we numerically examine the general equilibrium costs of an
environmental tax reform. In addition, we also consider the costs of alternative revenuerecycling schemes and grandfathered tradable permits. The simulation model reproduces
the key analytical results derived above and provides magnitudes of the effects of
alternative scenarios under large policy changes. Subsections A and B present the
functional forms and calibration, respectively.
A. Functional Forms
The representative household's utility is given by the nested constant elasticity of
substitution (CES) utility function:
U = UC C
U 1
U
+ Ul l
U 1
U
U
U 1
(E)
(3.1)
C
C 1
C 1
C
+ CY Y
C = CX X
C 1
C
(3.2)
15
where l is the household's consumption of leisure and C is the part of utility derived from
consumption of goods. Y is a clean good representing the majority of consumption and X
is a polluting good. U and C are the elasticities of substitution between goods and
leisure and between the consumption of X and Y respectively. The parameters control
the share of total income spent on leisure and each of the goods. Note that disutility from
emissions, E, is separable and given by the function (E), where '>0 and ''0.
There are two notable restrictions implied by the form of utility.
First, the
separability of environmental damage rules out any interaction between emissions and
labor/leisure and consumption tradeoffs made by the household. Second, the nesting of
the clean and dirty goods in C implies that they are equal substitutes for leisure.
Production of the clean good is as in a standard one factor model, while
production of the dirty good, X, is given by a CES production function incorporating
labor and a fixed factor F:
Y = LY
X = X LX LX
(3.3)
X 1
X
+ FX F
X 1
X
X
X 1
(3.4)
X is the elasticity of substitution between labor and the fixed factor in the production of
X. In our analysis, we will vary the scale parameter for F; note that in the limiting case
when FX = 0 the model reduces to the usual one factor case. Production of both goods is
constant returns to scale and pollution is proportional to the production of the dirty good.
The final agent is government, which provides a transfer G to households. We
extend the analytical model and consider the case where the government levies three
16
taxes: a labor tax, L, a tax on the fixed factor, F, and a tax on emissions, E. We assume
the government budget is kept in balance by:
G = L L + F PF F + E E
(3.5)
For our central simulations the government holds G fixed in real terms and
balances the budget by adjusting L. The pre-existing tax levied on the fixed factor is
held constant for any given policy, but varied in a sensitivity analysis. In order to isolate
the revenue recycling effect and provide a larger variety of policies, we also include
alternate simulations where factor taxes are held fixed and the government returns
additional revenue from the emissions tax lump sum.
The numerical model is solved by setting prices and taxes such that the
government budget balances, the desired emissions level is reached, and the factor
markets clear. The government budget is given above and emissions are set by adjusting
the level of E. The labor market equilibrium is given by:
L = L X + LY
(3.6)
where the supply of labor and demands for the two goods are given by the solution to the
household's problem which consists of maximizing (3.1) subject to the budget constraint:
p X X + Y (1 L ) L + (1 F ) p F F + G
(3.7)
Firms choose inputs to minimize production costs which determines the producer
prices of X and Y and demands for inputs. Demand and supply of inputs and goods is
equated in equilibrium.
B. Model Calibration
17
The elasticity of substitution between consumption of goods and leisure (U) is
calibrated to be consistent with econometric evidence of labor supply elasticities. In our
very aggregate model, this elasticity will represent the total supply response of labor in
terms of hours worked and participation rates averaged across the labor force. In order to
make the model consistent with estimates of both compensated and uncompensated
elasticities, we use both the elasticity parameter U and the initial ratio of total time
endowment to labor supply ( L L ) for calibration. We use values of 0.15 and 0.40 for the
uncompensated and compensated elasticities respectively, approximating the mean values
reported in Fuchs et al. [4].11 Following earlier studies (e.g. Goulder et. al. [6]), we
assume a benchmark distortionary labor tax rate (L) of 40 percent. This is meant to
include the combined effects of personal, payroll, and sales taxes.
Since our results will depend heavily on the relative size of the polluting sector
(X) and the fraction of input coming from a fixed factor (FX), we let this vary in the
sensitivity analysis. The calibration for the central case, however, is meant to roughly
reflect the size and composition of the United States electricity market. We take the
electricity sector to be 2.7 percent of the economy, consistent with aggregate data from
the Department of Energy.12 Values of 1 and 10 percent are considered in the sensitivity
analysis.
The relative size of the fixed factor in the central case is taken to be 25 percent,
based on the approximate value of the fossil fuel used in U.S. electricity generation.
Table 1 shows a decomposition of generation expenses, supporting this central case
11
Goulder et. al. [6] also calibrates their model to these values for the labor supply elasticities.
1996 electricity sales of $212 billion (Electric Power Annual 1996, DOE/EIA-0348(96)/1, August 1997.)
divided by 1996 US GDP ($7,813 billion).
12
18
estimate. The fraction of electricity generation expenses that represent Ricardian rents to
a fixed factor is one of the most important parameters in our analysis and one of the least
well agreed upon. In order to make the analysis as broadly applicable as possible, we
consider a large range for this parameter letting the size of the fixed factor vary between
0 and 50 percent. Preexisting rent taxes (F) play an opposite but very similar role to the
size of the fixed factor, effectively reducing the amount of rents remaining in the resource
sector. We set these to 10 percent in the benchmark, as a rough approximation to United
States resource royalties.
Low and high values of zero and 40 percent are also
presented.13
Our example of electricity production and fossil fuel is one of several cases where
environmental taxes might be levied in the presence of a factor earning Ricardian rents.
Another example is the cement industry, which produces substantial environmental
externalities and employs large quantities of mineral resources. Similarly, taxes on the
steel industry could fall partially on rent-earning iron ore resources. Finally, not all fixed
factors earning Ricardian rents need be natural resources: Our analysis could also apply
to quasi-fixed capital, such as a fully depreciated power plant, earning this type of rents.
The elasticity of substitution in the production of the polluting good (X) is
initially set to unity; a halving and doubling of this to 0.5 and 2.0 are considered in the
sensitivity analysis. Similarly, the consumption elasticity of substitution between the two
13
The situation where the government cannot extract any of the rents through taxation could represent less
developed regions where competition among countries absorbs all the rents, although this issue may present
further distortion that we are unable to consider.
19
goods (C) in the economy is set to unity in the benchmark. The assumption on these two
elasticities is standard given the aggregate nature of the model.14
4. Results
This section presents our simulation results illustrating how the presence of fixed
factors in the production of polluting goods and Ricardian rents affects the price of the
polluting good, the costs, overall welfare impacts, and optimal levels of environmental
policies.
A. Impact of the fixed factor on the price of the polluting good
In figure 1 we compare the increase in the price of the polluting good (due to the
environmental tax) in our model relative to models that do not incorporate a fixed factor
in production.
P NFF indicates the increase in the price when we set the value of the fixed factor equal
to zero. This curve has a zero intercept, and is given by the 45-degree line, suggesting
that, in a world without a fixed factor in the production of the polluting good, the impact
of the environmental tax is to raise the price of the polluting good by the full amount of
the tax. Thus, for example, a 10 percent increase in the tax translates to a 10 percent
increase in the price of the polluting good.
p FF shows the increase in price of the polluting good in the presence of a fixed factor.
This curve lies below the 45-degree line. The difference between p FF and p NFF confirms
14
Goulder et. al. [6] choose slightly lower elasticities of 0.9 for input substitution and 0.85 for substitution
between the final goods. We consider values as low as 0.5 in our sensitivity analysis and find that changing
these elasticities has little effect on our results.
20
that, in the presence of the fixed factor, part of the burden of the environmental tax will
fall on the fixed factor, and hence, the overall increase in the price of the polluting good
will be lower. Our model suggests that roughly 85 percent of the tax is passed to
consumers in the form of higher prices while the remaining 15 percent falls on the fixed
factor.
B. Marginal Costs
In figure 2 we compare the marginal cost of reducing pollution under different
scenarios for revenue-recycling. Marginal costs are expressed as a percent of the initial
value of income in the economy.
MC PRIM 0 indicates marginal costs in a first-best case when we set pre-existing taxes
and the level of the fixed factor to zero. This curve reflects the primary economic costs of
the environmental tax. MC PRIM 0 has a zero intercept, and is upward sloping, reflecting the
increasing marginal cost of substituting other goods and leisure for the polluting good.
MC PRIM FF shows the marginal costs when we include the fixed factor in the model,
but still set labor taxes at zero. The difference between MC PRIM FF and MC PRIM 0 isolates
the importance of the fixed factor to the magnitude of the primary costs of the policy.
This difference suggests that the presence of fixed factor in the production of the
polluting good indeed increases the primary costs of the environmental tax. For example
at 30 percent emissions reduction, the difference in cost is about 20 percent, and reflects
the fact that, in the presence of a fixed factor, in order to achieve the same emissions
reductions, the level of the environmental tax needs to be higher.
21
MC LS FF shows the marginal costs of the environmental tax with a pre-existing
labor tax but no revenue-recycling effect; in this case, the revenues generated by the
environmental tax are neutralized by adjusting the lump-sum transfer. The difference
between this curve and MC PRIM FF isolates the importance of the tax-interaction effect for
the costs of the policy. This effect causes a substantial upward shift of the marginal cost
curve (see Goulder et al. [6] for more discussion). For example, at 30 percent emissions
reduction, the difference in cost is about 40 percent.
MC RRFF shows the marginal cost under the pollution tax with revenues used to
reduce the labor tax. It equals MC LS FF net of the benefit from the revenue-recycling effect.
A novel aspect of this curve is its negative intercept. In fact, it is the case that marginal
costs are negative up to about 6 percent. The environmental tax essentially allows the
burden of the tax system to shift away from labor towards the fixed factor in the
economy. Therefore, up to a point, the environmental tax reform reduces the overall costs
of the tax system, not counting environmental benefits. Also, note that MC RRFF crosses
MC PRIM 0 at 12 percent emissions reductions reflecting the fact that interactions with the
tax system lower the costs of environmental taxes up to 12 percent. However, MC RRFF
eventually converges to MC LS FF suggesting an erosion of the tax base and an increase in
distortions as emissions reduction levels increase.
C. Total Costs
We now consider the total costs of emissions reductions. Like in the previous figure,
we compare how the costs are sensitive to the introduction of the fixed factor in the
model and the mechanism of revenue-recycling. In addition, we also provide a
22
comparison between (partially) grand-fathered tradable permits and environmental taxes.
Total costs are expressed relative to total primary cost. When a curve lies above (below)
unity, the net impact of interactions with the tax system is to raise (lower) the overall cost
of the policy above (below) its primary costs.
The most novel feature of figure 3 is the total cost curve for the environmental tax in
the presence of a fixed factor, with revenues used to reduce the labor tax. This curved,
denoted by TC RRFF , lies below the horizontal axis for emission reductions up to 12
percent. When total costs are negative the welfare gain from reducing the costs of the tax
system is more than offsetting the primary cost of the policy. In his reader’s guide
Goulder [5] refers to this as a “strong” form of a double dividend from environmental tax
reform; even without accounting for the environmental gain, the policy increases overall
welfare. When total costs are positive but less than primary cost (indicated at unity on our
figure), there is still a net welfare gain from interactions with the tax system. In our
central parameter case, we find that this intermediate form of the double dividend occurs
up to 23 percent of emissions reductions. For emission reductions greater than 23 percent,
the costs of the policy are higher than the primary costs, suggesting that the rents from
the fixed factor are exhausted. At this point, the exacerbation of the distortion in the labor
market begins to dominate.
If we remove the fixed factor from the model, the total cost of an environmental tax,
when revenues are used to cut labor taxes, will now be above unity. TC RR0 illustrates this
situation. In this case there is no potential for a double dividend; the general equilibrium
costs of this policy exceed primary costs by around 30 percent. Figure 3 clearly shows
that – by neglecting the potential existence of fixed factors in the production of polluting
23
goods and the possibility of environmental taxes to serve as rent taxes – the magnitude of
costs of environmental tax reforms may be substantially overstated, and possibly of the
opposite sign. For example, for a reduction in emissions of about 15 percent, models not
considering a fixed factor might estimate costs equal to 133 percent of primary costs; in
contrast our analysis predicts a welfare gain equal to 50 percent of primary costs. The
magnitude of this effect will depend directly on how important the rent-earning fixed
factor is in production. Because of this important relationship, we later let the size of the
fixed factor vary smoothly between 0 and 50 percent of the cost of production in our
sensitivity analysis. 15
When the revenues from the environmental tax are neutralized by lump-sum
transfers, total costs are given by TC LS0 for a model without a fixed factor and by
TC LS FF for a model with a fixed factor. By comparing these two curves, one can conclude
that the costs of the environmental tax are higher in the presence of the fixed factor
because the need for a higher tax creates some additional distortions in the economy.
D. Optimal Policies
To calculate optimal second best emissions reductions, we postulate different values
for the marginal environmental benefit from reducing pollution. In Figure 4, along the
horizontal axis we measure Pigouvian emissions reduction and on the vertical axis the
optimal second best pollution reduction (relative to Pigouvian reductions)
15
Notice that a case where only partial rents are earned would be modeled in our framework as one where
the size of the fixed-factor in production is proportionately smaller. Labor costs (of extraction, for
example) are netted out when determining how large the fixed factor is.
24
Again, the novel feature of this figure is the curve for the pollution tax in the presence
of a fixed factor, W RRFF . Over an initial range, this curve lies above unity, while the
curves for all other policies lie below unity. This suggest that, up to 11 percent emissions
reduction, the optimal second best environmental tax should be higher that the Pigouvian
tax. This result re-enforces the importance of the rent effect in equation (2.9) in the
analytical model. In fact, up to 11 percent, the rent effect fully dominates the tax
interaction effect.
E. Varying the Size of the Fixed Factor
As mentioned, the importance of a fixed factor (perhaps measured as the share of
remaining Ricardian rents in electricity cost) is difficult to estimate and subject to debate.
In order to address this, we now vary the share of the fixed factor in the production of the
polluting good over the range zero to 50 percent. We then measure the total costs of
policies for a fixed reduction in emissions of 10% and present the results in figure 5.
The curve TC RR shows the total costs of reducing emissions under the environmental
tax, when revenues are recycled to cut pre-existing labor taxes. We note that, as the
percent of fixed factor in the polluting good rises, the total cost of the policy falls
relatively sharply. The costs of the policy actually become negative when the share of
fixed factor is higher than 22 percent. If, on the other hand, we totally eliminate the fixed
factor from the model, the costs of the policy are about 133 percent of the primary costs,
a result which is consistent with previous studies (see e.g., Goulder et al. [6]).
The curve TC LS shows the total cost of the emissions tax, when the revenues are
returned in a lump sum fashion. The increasing availability of the Ricardian rents no
25
longer reduces the cost of policy, but in fact causes a slight increase in cost as the tax rate
required to achieve a 10% emissions reduction increases.
In the case where some of the emissions permits are grandfathered (TCPERM) we see
that costs are initially higher than in the lump sum case but then begin to fall. This
reflects the growing amount of emissions tax revenue coming from Ricardian rents while
the fraction of total revenue grandfathered remains constant. As the Ricardian rents
become very important they begin to offset the losses from grandfathering, although of
course at a slower rate than the TCRR case where no permits are grandfathered.
F. further sensitivity analysis
We end this section by exploring the sensitivity of the above results to some
additional parameter variation. We focus on the cases where a change in the parameters
would likely affect the magnitude of the efficiency channels embedded under the
different policies and we include the benchmark as the reference case. In particular we
vary the size of the polluting industry, the fraction of the fixed factor in the polluting
industry, the pre-existing tax on the fixed factor and the elasticity of substitution in
production between labor and the fixed factor. Table 2 summarizes the results of the
sensitivity analysis.
(i) varying the size of the polluting industry: In the third row in table 2, we vary the
size of the polluting industry between 1 percent (low) and 10 percent (high). We remind
the reader that in the central case, we have assumed that the size of the polluting industry
was 2.7 percent. Varying the size of the polluting industry scales total costs but the ratio
of second best to primary costs remains roughly constant. For a 10 percent emissions
26
reductions this ratio is -0.17 in the central case and it varies between -0.18 and -0.13 in
the low and high scenarios. Similarly, for 50 percent emissions reductions, in the central
case the ratio of second best costs to primary cost is 1.37 while in the low and high
scenarios is 1.37 and 1.39 respectively.
(ii) varying the fraction of fixed factor in the polluting industry : In the forth row in
table 2, we vary the fraction of the fixed factor in the polluting industry between 12.5
percent (low case) and 50 percent (high case). The central value was 25 percent. Not
surprisingly, our results are very sensitive to the share of fixed factor in the production of
the polluting good, reflecting the fact that the amount of rent available in the economy
varies with this parameter.
(iii) varying the pre-existing tax on rents from fixed factor: In the fifth row in table 2,
we vary the pre-existing tax on the fixed factor between 0 and 40 percent. Increasing the
pre-existing tax on the rents from the fixed factor, increases dramatically the ratio of
second best costs to primary cost. An increase in the pre-existing tax essentially uses up
some of the resource rents and eliminates the possibility for the environmental tax to
swap burden away from the labor market towards the Ricardian rent.
(iv) varying the elasticity of substitution in the production of the polluting good: In
the last row in table 2, we vary the elasticity of substitution in the production of the
polluting good between 0.5 and 2. Varying this parameter highlights two interesting
results. First, at 10 percent emissions reductions, increasing the elasticity of substitution
reduces the rents from the fixed factor and, in turn, increases the ratio of second best cost
to primary cost. Second, increasing the elasticity of substitution also decreases the costs
27
of substitution for higher levels of emissions reductions. Therefore the ratio of second
best total cost to primary cost at 50 percent is actually lower in the high elasticity case.
We conclude this section by noting the following two additional points. At 10 percent
emissions reductions, the cost ratio is quite sensitive to the choice of parameter values.
However, as the level of emissions reductions increases, the ratios converge to the results
presented in Goulder et. al. [6], a reflection of the dominance of the traditional tax
interaction effect. Second, for moderate levels of emissions reduction, the second best
cost with a fixed factor and revenue-recycling is always cheaper than primary costs,
suggesting a potential for a double-dividend to occur.
5. Conclusions
This paper uses simple analytical and numerical simulation models to demonstrate the
potential importance of fixed-factors and Ricardian rents in the production of polluting
goods for the general equilibrium welfare effects of environmental policies. In the
presence of fixed factors in the production of polluting goods and (partially) untaxable
Ricardian rents, a tax system consisting of a labor tax is not optimal to begin with, even
from a non-environmental perspective. In this setting the welfare gain from introducing
an environmental tax with revenues used to cut pre-existing labor taxes can be
significantly higher than implied by earlier models. In fact, under certain conditions, the
overall costs of an environmental tax swap can be negative and produce a strong double
dividend. In our simulations, this was the case up to 11 percent of emissions reductions.
This result has clear implications for policy analysis and suggests that even in the absence
of clear evidence about the benefits from emissions reductions, the environmental tax
28
should be part of the tax system. Our results also suggest that the cost savings from using
revenue-neutral environmental taxes over non-auctioned pollution permits can be
dramatically higher than suggested in previous literature.
In some sense our results highlight the tradeoffs between primary costs, first, and
second dividends of environmental policies. From an environmental perspective, the
presence of fixed factors in the production of polluting goods can compromise the
magnitude of the first dividend, simply because part of the tax falls on the fixed factor
and the price of the polluting good doesn’t increase by the full amount of the
environmental tax. However, and for the exact same reason, the environmental tax swap
reduces the overall cost of the tax system because it shifts the burden away from labor
towards the fixed factor, producing a positive second dividend.
Acknowledgments
We thank Lawrence Goulder, Rob Williams, the two referees and the editor for
very helpful comments.
References
[1] A. L. Bovenberg and R.A. de Mooij, Environmental Levies and Distortionary
Taxation, American Economic Review 84 (1994) 1085-1089.
[2] A. L. Bovenberg and L. H. Goulder, Optimal Environmental Taxation in the presence
of Other Taxes: General Equilibrium Analyses, American Economic Review 86 (1996)
985-1000.
[3]A. L. Bovenberg and L. H. Goulder, Environmental Taxation, in A. Auerbach and M.
Feldstein, eds., Handbook of Public Economics, New York, North Holland, 2002, 14711547.
[4] V. R. Fuchs, A. B. Krueger, and J. M. Poterba, Economists’ Views About Parameters,
Values and Policies: Survey results in labor and public economics, Journal of Economic
Literature 36(3) (1998) 1387-1425.
[5] L. H. Goulder, Environmental Taxation and the ‘Double Dividend’: A Reader’s
Guide, International Tax and Public Finance 2 (1995) 157-198
29
[6] L. H. Goulder, I.W. H. Parry, R. C. Williams and D. Burtraw, The Cost-Effectiveness
of Alternative Instruments for Environmental Protection in a Second Best Setting, Journal
of Public Economics 72 (1999) 329-360.
[7] E. Koskela. R. Schon and H. Sinn, Pollution, Factor Taxation and Unemployment,
International Tax and Public Finance 5(3) (1998) 379-396.
[8] I. W. H. Parry, Pollution Taxes and Revenue Recycling, Journal of Environmental
Economics and Management 29 (1995) S64-77.
[9] I. W. H. Parry, R. C. Williams and L. H. Goulder, When Can Carbon Abatement
Policies Increase Welfare? The Fundamental Role of Distorted Factor Markets, Journal of
Environmental Economics and Management 37 (1999) 52-84.
[10] I. W. H. Parry and A. M. Bento, Environmental Policy, Tax Deductions and the
Double Dividend Hypotheses, Journal of Environmental Economics and Management 39
(2000) 67-96.
[11] I. W. H. Parry and A. M. Bento, Revenue Recycling and the Welfare Effects of Road
Pricing, Scandinavian Journal of Economics 103 (2001) 645-671.
[12] C. Perroni and J. Whalley, Rents and the Cost and Optimal Design of Commodity
Taxes, The Review of Economics and Statistics 80(3) (1998) 357-364.
[13] R. C. Williams, Revisiting the Cost of Protectionism: The Role of Tax Distortions in
the Labor Market, Journal of International Economics 47 (2) (1999) 429-447.
[14] R. C. Williams, Environmental Tax Interactions when Pollution Affects Health and
Productivity, Journal of Environmental Economics and Management 44 (2002) 261-270.
[15] R. C. Williams, Health Effects and Optimal Environmental Taxes, Journal of Public
Economics 87(2) (2003) 323-335.
30
Table1. Fraction of fuel costs in electricity production
Investor
Owned
Electric Utilities
Share of US Electricity Sales
1
Fuel Purchases
As % of Operation and
2
Maintenance Costs
3
As % of Total Expenses
Estimated Fuel Costs Net of
4
Refining and Transportation
As % of Operation and
Maintenance Costs
As % of Total Expenses
Publicly
Owned
Total
76%
15%
91%
40.3%
28.8%
39.1%
24.8%
20.2%
24.4%
31.0%
22.2%
30.1%
19.1%
15.6%
18.7%
1
Remaining 9% is from cooperatives and federal utilities
Includes all electricity generation, transmission and distribution costs
3
Includes operation and maintenance plus depreciation, amortization, and taxes
4
Based on fuel share weighted ratio of wellhead (minemouth) price of gas (coal) to delivered
price of 0.77
2
Financial Statistics of Major U.S. Investor Owned Electric Utilities 1996, U.S. Department
of Energy DOE/EIA-0437(96)/1, December 1997.
Financial Statistics of Major U.S. Publicly Owned Electric Utilities 1996, U.S. Department
of Energy DOE/EIA-0437(96)/2, March 1998.
31
Table 2: Ratio of "Second Best" Total Cost to Primary Cost
Pollution Reduction
10%
25%
50%
Central Case
-0.17
1.03
1.37
-0.18
-0.13
0.66
-2.89
-0.37
0.45
-1.36
0.51
1.02
1.07
1.18
0.62
0.96
1.24
0.91
1.13
1.37
1.39
1.33
1.54
1.35
1.45
1.45
1.33
Size of polluting industry
Fraction fixed factor in
polluting industry
Preexisting tax on fixed
factor
Elasticity of subs. in
production
Low
High
Low
High
Low
High
Low
High
32
Figure 1: Price Effect of Emissions Tax on Polluting Good
Increase in Price of Polluting Good..
1.0
0.8
0.6
P NFF
P FF
0.4
0.2
0.0
0.0
0.2
0.4
0.6
Tax on Polluting Good
33
0.8
1.0
Figure 2: Marginal Cost of Emissions Reductions
0.12
Marginal Cost (% of Income)
0.10
0.08
0.06
MC LS FF
MC PRIM FF
0.04
MC PRIM 0
0.02
0.00
MC RR FF
-0.02
0
10
20
30
Percent Emissions Reduction
34
40
50
Figure 3: Total Cost of Emissions Reduction
Total Cost (relative to primary cost) .
5
4
TC PERM FF
3
TC LS 0
TC LS FF
2
TC RR 0
1
0
TC RR FF
-1
-2
0
10
20
30
Percent Emissions Reduction
35
40
50
Optimal Second Best Reductions
(Relative to Pigouvian Level)
Figure 4: Optimal Policy Relative to Pigouvian Level
2
W RR FF
1
W PRIM FF
W LS FF
W PERM FF
0
0
10
20
30
40
Pigouvian Emissions Reduction (%)
36
50
Total Cost Ratio at 10% Emissions Reduction
.
Figure 5: Total Cost at 10% Abatement, Varying Size of Fixed Factor
5
4
TC LS
TC PERM
3
2
TC RR
1
0
0%
10%
20%
30%
40%
-1
-2
Percent of Fixed Factor in Polluting Good
37
50%